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A minimal predicative set theory. (English) Zbl 0816.03023
The authors choose a very weak set theory, denoted by N, having just the following axioms: (1) \(\emptyset\) exists, and (2) for any two sets \(x\), \(y\), \(x\cup \{y\}\) exists, and prove that Robinson’s arithmetic Q is interpretable in N. This is to be understood as a reasonable reduction from the point of view of Hilbert’s Program, which continues analogous work of E. Nelson. The proof of the interpretability of Q into N is given through a large number of steps which are a bit difficult to follow. A finistic proof of Herbrand consistency of N is also given.

03E70 Nonclassical and second-order set theories
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